Texas 41
Oklahoma St. 36

STILLWATER, Okla. — David Ash threw three touchdown passes to Jaxon Shipley and Joe Bergeron scored on a 2-yard run with 29 seconds left to lift No. 12 Texas to a 41-36 win over Oklahoma State on Saturday night.

Ash directed the Longhorns (4-0, 1-0 Big 12) on a 75-yard scoring drive after the Cowboys (2-2, 0-1) had taken the lead on Quinn Sharp’s 23-yard field goal with 2:34 to play.

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Ash connected with tight end D.J. Grant for a 29-yard pickup on fourth and 4 to keep the drive going, and then Mike Davis outleaped Justin Gilbert on a 32-yard deep ball to set up Bergeron’s winning touchdown.

‘‘[Ash] will not be under any more pressure than this, and he couldn’t have done this this time last year,’’ said coach Mack Brown, who moved to 7-0 in Stillwater. ‘‘He has really grown up. He is the leader of this football team.’’

J.W. Walsh started in place of injured Oklahoma State quarterback Wes Lunt and threw for 307 yards and two TDs.

Joseph Randle added a career-high 199 yards rushing and two touchdowns for the Cowboys, who hung a banner marking last season’s Big 12 championship but started their defense of it by coming up short in a wild fourth quarter that featured four lead changes.

The Longhorns had lost at home to OSU each of the past two seasons. Last season, Ash was making his first career start and struggled in a loss.

‘‘That game really haunted me because as a first start, it wasn’t the first start that you wanted to have,’’ said Ash, who finished with 304 yards passing and threw his first pick of the season.

‘‘This game kind of means a lot.’’

Randle lunged in from 2 yards out to put Oklahoma State up, 33-28, early in the fourth, only for Texas’s potent running game to come alive next. Bergeron also capped that 75-yard drive with a 2-yard touchdown run, as the Longhorns picked up 65 yards on seven carries while moving down the field.

After the ensuing kickoff went out of bounds, Oklahoma State needed just three plays to bolt to the Texas 13-yard line. That drive stalled, with three straight 2-yard runs — two by third-stringer Desmond Roland and then one by Randle, who was given a breather.

Sharp’s field goal put the Cowboys back on top — but there was just enough time for Ash to lead the Longhorns back.

Bergeron’s scoring run was reviewed on instant replay after Oklahoma State safety Daytawion Lowe came out of the pile with the ball in the end zone, but officials upheld the call on the field.

Ash also threw TD passes of 44 and 20 yards to Shipley in the first half before hooking up for a 7-yard TD on a fade in the third quarter to make it 28-20.

Walsh rallied Oklahoma State with a 20-yard TD pass to John Goodlett at the tail end of the third quarter to start an Oklahoma State rally and set up the fourth-quarter theatrics.

Walsh also had a 44-yard TD pass to former high-school teammate Josh Stewart in the first half.

Randle took a handoff on the second play of the game and shed a tackle attempt by Adrian Phillips on his way for a 69-yard scoring run. Phillips also missed a tackle on Stewart’s 44-yard touchdown catch as the Cowboys tied it at 14.

D.J. Monroe ran back the ensuing kickoff 100 yards for the go-ahead score.